An iterative row-action method for interval convex programming

  • Y. Censor
  • A. Lent
Contributed Papers

DOI: 10.1007/BF00934676

Cite this article as:
Censor, Y. & Lent, A. J Optim Theory Appl (1981) 34: 321. doi:10.1007/BF00934676


The iterative primal-dual method of Bregman for solving linearly constrained convex programming problems, which utilizes nonorthogonal projections onto hyperplanes, is represented in a compact form, and a complete proof of convergence is given for an almost cyclic control of the method. Based on this, a new algorithm for solving interval convex programming problems, i.e., problems of the form minf(x), subject to γ≤Ax≤δ, is proposed. For a certain family of functionsf(x), which includes the norm ∥x∥ and thex logx entropy function, convergence is proved. The present row-action method is particularly suitable for handling problems in which the matrixA is large (or huge) and sparse.

Key Words

Interval convex programming entropy optimization large and sparse matrices nonorthogonal projections image reconstruction from projections 

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • Y. Censor
    • 1
  • A. Lent
    • 1
  1. 1.Medical Image Processing Group, Department of Computer ScienceState University of New York at BuffaloAmherst
  2. 2.Department of MathematicsUniversity of Haifa, Mt. CarmelHaifaIsrael
  3. 3.New Ventures, Technicare CorpCleveland

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